Abstract: To solve the problems of the traditional AHP method which needs to satisfy the consistency condition in constructing judgment matrixes, the reasons of consistency regulation from AHP are studied and an inconsistency judgment matrix ranking method based on manifold learning is proposed in this paper. In the ranking process of inconsistency judgment matrixes, on the basis of the neighbor distance, the neighbor distance matrixes of the data sets corresponding to judgment matrixes are constructed firstly. Next each data point is mapped to a low-dimensionally global coordinate system based on the linear representations of the neighbor points, and the low-dimensional embeddings that correspond to judgment matrixes are obtained. Then the ranking conclusion is gotten by analyzing the superiority and inferiority ranking of the elements according to the correspondingly calculated low-dimensional embeddings from each hierarchy. Finally, a numerical example illustrates that the proposed method has a higher level of effectiveness and practicability.

Key words: analytic hierarchy process, manifold learning, judgment matrix, consistency check, ranking method